Question: A circle with circumference $16\pi$ has an arc with a $240^\circ$ central angle. What is the length of the arc? ${16\pi}$ ${240^\circ}$ $\color{#DF0030}{\dfrac{32}{3}\pi}$
Answer: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{240^\circ}{360^\circ} = \dfrac{s}{16\pi}$ $\dfrac{2}{3} = \dfrac{s}{16\pi}$ $\dfrac{2}{3} \times 16\pi = s$ $\dfrac{32}{3}\pi = s$